What are the solutions to the equation 780n^2+26n^3=2999134 ?

The solutions to the equation 780n^2+26n^3=2999134 are n\approx 40.46101…

Find the zeros of 780n^2+26n^3=2999134

The zeros of 780n^2+26n^3=2999134 are n\approx 40.46101…

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780 n^{2} + 26 n^{3} = 2999134

n \approx 40.46101 \dots

Solution steps

780 n^{2} + 26 n^{3} = 2999134

Move

2999134

to the left side

780 n^{2} + 26 n^{3} - 2999134 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

26 n^{3} + 780 n^{2} - 2999134 = 0

Find one solution for

26 n^{3} + 780 n^{2} - 2999134 = 0

using Newton-Raphson:

n \approx 40.46101 \dots

Apply long division:

\frac{26 n ^{3} + 780 n ^{2} - 2999134}{n - 40.46101 \dots} = 26 n^{2} + 1831.98646 \dots n + 74124.03724 \dots

26 n^{2} + 1831.98646 \dots n + 74124.03724 \dots \approx 0

Find one solution for

26 n^{2} + 1831.98646 \dots n + 74124.03724 \dots = 0

using Newton-Raphson:

No Solution for

n \in R

The solution is

n \approx 40.46101 \dots

x^{3} - 3 x^{2} - 41 x = 0

y^{3} y - 10 = 3

- 24 x^{120} = - x

y = y^{3}

5 n x^{4} (\frac{1}{5})^{3} = 125

What are the solutions to the equation 780n^2+26n^3=2999134 ?
The solutions to the equation 780n^2+26n^3=2999134 are n\approx 40.46101…
Find the zeros of 780n^2+26n^3=2999134
The zeros of 780n^2+26n^3=2999134 are n\approx 40.46101…